I am trying to do the following integration:
Ld = 2;
a1 = 0.3;
a2 = 1;
potd[R_, z_] =
-Integrate[(0.5/(2*a1)*Exp[-(Abs[z1]/a1)] +
0.5/(2*a2)*Exp[-(Abs[z1]/a2)])*
Integrate[
BesselK[0, a/Ld]*a*
ArcSin[(2*a)/(
Sqrt[(z - z1)^2 + (a + R)^2] +
Sqrt[(z - z1)^2 + (a - R)^2])], {a, 0, Infinity},
GenerateConditions -> False], {z1, -Infinity, Infinity},
GenerateConditions -> False];
then I evaluate the result for different pairs of R
, z
.
Mathematica complains that
NIntegrate::inumr: The integrand a ArcSin[(2 a)/(Sqrt[Power[<<2>>]+Power[<<2>>]]+Sqrt[Power[<<2>>]+Power[<<2>>]])] BesselK[0,a/2] has evaluated to non-numerical values for all sampling points in the region with boundaries {{∞,0}}. >>
The point is that there is no NIntegrate
: what does it mean?
I upload the function from my notebook so you can see that I am not using a NIntegrate
.
a1 = 3/10
? It might help to indicate specificR
,z
that give the message. $\endgroup$0.5
anda1
. If they are changed to exact numbers1/2
and1/3
, theNIntegrate
messages do not appear. (FWIW, M tries to evaluateNIntegrate[a ArcSin[(2 a)/(Sqrt[(a - R)^2 + (z - z1)^2] + Sqrt[(a + R)^2 + (z - z1)^2])] BesselK[0, a/2], {a, 0, ∞}, WorkingPrecision -> 30.9546, AccuracyGoal -> ∞, PrecisionGoal -> 20.9546]
, which is foolish becauseR
andz
are symbols.) $\endgroup$